A Multiphysics Biventricular Cardiac Model: Simulations With a Left-Ventricular Assist Device

Computational modeling of cardiac hemodynamics including chordae tendineae, papillaries, and valves dynamics

In the context of dynamic image-based computational fluid dynamics (DIB-CFD) modeling of cardiac system, the role of sub-valvular apparatus (chordae tendineae and papillary muscles) and the effects of different mitral valve (MV) opening/closure dynamics, have not been systemically determined. To provide a partial filling of this gap, in this study we performed DIB-CFD numerical experiments in the left ventricle, left atrium and aortic root, with the aim of highlighting the influence on the numerical results of two specific modeling scenarios: (i) the presence of the sub-valvular apparatus, consisting of chordae tendineae and papillary muscles; (ii) different MV dynamics models accounting for different use of leaflet reconstruction from imaging. This is performed for one healthy subject and one patient with mitral valve regurgitation. Specifically, a systolic wall motion is reconstructed from dynamic Cine-MRI images and imposed as boundary condition for the CFD numerical simulation. Analyzing the numerical results, we found that sub-valvular apparatus do not affect the global fluid dynamics quantities, although it creates local variations, such as the developing of vortexes or flow disturbances, which lead to different stress distributions on cardiac structures. Moreover, different MV dynamics are considered starting from Cine-MRI MV segmentation at different temporal configurations, and then they are compared and managed numerically through a resistive approach. The obtained results highlight the importance of including a sophisticated diastolic model of MV dynamics, which accounts for MV geometries during diastasis and A-wave, in terms of describing the disturbed flow and ventricular turbulence.

Algorithmic Generation of Parameterized Geometric Models of the Aortic Valve and Left Ventricle

Simulating the cardiac valves is one of the most complex tasks in cardiovascular modeling. As fluid-structure interaction simulations are highly computationally demanding, machine-learning techniques can be considered a good alternative. Nevertheless, it is necessary to design many aortic valve geometries to generate a training set. A method for the design of a synthetic database of geometric models is presented in this study. We suggest using synthetic geometries that enable the development of several aortic valve and left ventricular models in a range of sizes and shapes. In particular, we developed 22 variations of left ventricular geometries, including one original model, seven models with varying wall thicknesses, seven models with varying heights, and seven models with varying shapes. To guarantee anatomical accuracy and physiologically acceptable fluid volumes, these models were verified using actual patient data. Numerical simulations of left ventricle contraction and aortic valve leaflet opening/closing were performed to evaluate the electro-physiological potential distribution in the left ventricle and wall shear stress distribution in aortic valve leaflets. The proposed synthetic database aims to increase the predictive power of machine-learning models in cardiovascular research and, eventually, improve patient outcomes after aortic valve surgery.

Advancement in computational simulation and validation of congenital heart disease: a review

The improvement in congenital heart disease (CHD) treatment and management has increased the life expectancy in infants. However, the long-term efficacy is difficult to assess and thus, computational modelling has been applied for evaluating this. Here, we provide an overview of the applications of computational modelling in CHD based on three categories; CHD involving large blood vessels only, heart chambers only, and CHD that occurs at multiple heart structures. We highlight the advancement of computational simulation of CHD that uses multiscale and multiphysics modelling to ensure a complete representation of the heart and circulation. We provide a brief future direction of computational modelling of CHD such as to include growth and remodelling, detailed conduction system, and occurrence of myocardial infarction. We also proposed validation technique using advanced three-dimensional (3D) printing and particle image velocimetry (PIV) technologies to improve the model accuracy.

A parametric study on pulse duplicator design and valve hemodynamics

BACKGROUND

In vitro assessment is mandatory for artificial heart valve development. This study aims to investigate the effects of pulse duplicator features on valve responsiveness, conduct a sensitivity analysis across valve prosthesis types, and contribute on the development of versatile pulse duplicator systems able to perform reliable prosthetic aortic valve assessment under physiologic hemodynamic conditions.

METHODS

A reference pulse duplicator was established based on literature. Further optimization process led to new designs that underwent a parametric study, also involving different aortic valve prostheses. These designs were evaluated on criteria such as mean pressure differential and pulse pressure (assessed from high-fidelity pressure measurements), valve opening and closing behavior, flow, and regurgitation. Finally, the resulting optimized setup was tested under five different hemodynamic settings simulating a range of physiologic and pathologic conditions.

RESULTS

The results show that both, pulse duplicator design and valve type significantly influence aortic and ventricular pressure, flow, and valve kinematic response. The optimal design comprised key features such as a compliance chamber and restrictor for diastolic pressure maintenance and narrow pulse pressure. Additionally, an atrial reservoir was included to prevent atrial-aortic interference, and a bioprosthetic valve was used in mitral position to avoid delayed valve closing effects.

CONCLUSION

This study showed that individual pulse duplicator features can have a significant effect on valve's responsiveness. The optimized versatile pulse duplicator replicated physiologic and pathologic aortic valve hemodynamic conditions, serving as a reliable characterization tool for assessing and optimizing aortic valve performance.

Exploring the influence of parametrized pulsatility on left ventricular washout under LVAD support: a computational study using reduced-order models

Introducing pulsatility in LVADs is known to reduce complications such as stagnation and thrombosis, but it is an ongoing topic of research on what the optimal form is. We present a framework consisting of parametrized full-order simulations, reduced-order models, and sensitivity analysis to systematically quantify the effects of parametrized pulsatility on washout. As a sample problem, we study the washout in an idealized 2D left ventricle and a parametrized sinusoidal LVAD flow rate. The framework yields speed-ups proportional to the number of samples required in the sensitivity analysis. In our setting, we find that short, intense pulses wash out the left ventricle best, while the time between consecutive pulses does not play a significant role.

The role of computational methods in cardiovascular medicine: a narrative review

Background and Objective

Computational models of the cardiovascular system allow for a detailed and quantitative investigation of both physiological and pathological conditions, thanks to their ability to combine clinical-possibly patient-specific-data with physical knowledge of the processes underlying the heart function. These models have been increasingly employed in clinical practice to understand pathological mechanisms and their progression, design medical devices, support clinicians in improving therapies. Hinging upon a long-year experience in cardiovascular modeling, we have recently constructed a computational multi-physics and multi-scale integrated model of the heart for the investigation of its physiological function, the analysis of pathological conditions, and to support clinicians in both diagnosis and treatment planning. This narrative review aims to systematically discuss the role that such model had in addressing specific clinical questions, and how further impact of computational models on clinical practice are envisaged.

Methods

We developed computational models of the physical processes encompassed by the heart function (electrophysiology, electrical activation, force generation, mechanics, blood flow dynamics, valve dynamics, myocardial perfusion) and of their inherently strong coupling. To solve the equations of such models, we devised advanced numerical methods, implemented in a flexible and highly efficient software library. We also developed computational procedures for clinical data post-processing-like the reconstruction of the heart geometry and motion from diagnostic images-and for their integration into computational models.

Key Content and Findings

Our integrated computational model of the heart function provides non-invasive measures of indicators characterizing the heart function and dysfunctions, and sheds light on its underlying processes and their coupling. Moreover, thanks to the close collaboration with several clinical partners, we addressed specific clinical questions on pathological conditions, such as arrhythmias, ventricular dyssynchrony, hypertrophic cardiomyopathy, degeneration of prosthetic valves, and the way coronavirus disease 2019 (COVID-19) infection may affect the cardiac function. In multiple cases, we were also able to provide quantitative indications for treatment.

Conclusions

Computational models provide a quantitative and detailed tool to support clinicians in patient care, which can enhance the assessment of cardiac diseases, the prediction of the development of pathological conditions, and the planning of treatments and follow-up tests.

Advancing clinical translation of cardiac biomechanics models: a comprehensive review, applications and future pathways

Cardiac mechanics models are developed to represent a high level of detail, including refined anatomies, accurate cell mechanics models, and platforms to link microscale physiology to whole-organ function. However, cardiac biomechanics models still have limited clinical translation. In this review, we provide a picture of cardiac mechanics models, focusing on their clinical translation. We review the main experimental and clinical data used in cardiac models, as well as the steps followed in the literature to generate anatomical meshes ready for simulations. We describe the main models in active and passive mechanics and the different lumped parameter models to represent the circulatory system. Lastly, we provide a summary of the state-of-the-art in terms of ventricular, atrial, and four-chamber cardiac biomechanics models. We discuss the steps that may facilitate clinical translation of the biomechanics models we describe. A well-established software to simulate cardiac biomechanics is lacking, with all available platforms involving different levels of documentation, learning curves, accessibility, and cost. Furthermore, there is no regulatory framework that clearly outlines the verification and validation requirements a model has to satisfy in order to be reliably used in applications. Finally, better integration with increasingly rich clinical and/or experimental datasets as well as machine learning techniques to reduce computational costs might increase model reliability at feasible resources. Cardiac biomechanics models provide excellent opportunities to be integrated into clinical workflows, but more refinement and careful validation against clinical data are needed to improve their credibility. In addition, in each context of use, model complexity must be balanced with the associated high computational cost of running these models.

Assessment of the elastic stiffness of human cardiac fibres after an apical infarction using finite element simulation

Several research works in the literature have focused on understanding the post-infarction ventricular remodelling phenomenon, but few works have considered the evaluation of the elastic behaviour of the cardiac tissue after a myocardial infarction. This paper presents an investigation focused on predicting the elastic performance of the human heart after a left ventricular apical infarction. The aim is to understand the elastic alterations of the cardiac fibres at different periods after an apical infarct. For this purpose, a hybrid method based on pressure and volume measurements of the left ventricle (LV) at different periods of ventricular remodelling, and the Finite Element Method (FEM), is developed. In addition, several performance indexes are defined to evaluate the heart performance during the ventricular remodelling process. The results show that during the first 2 weeks after a heart infarction, the cardiac fibres must support a much higher structural overload than during normal conditions. This structural overload is proportional to the aneurysm size but diminishes with the time, together with a significant reduction of the ventricular pumping capacity.

A sensorless, physiologic feedback control strategy to increase vascular pulsatility for rotary blood pumps

Continuous flow rotary blood pumps (RBP) operating clinically at constant rotational speeds cannot match cardiac demand during varying physical activities, are susceptible to suction, diminish vascular pulsatility, and have an increased risk of adverse events. A sensorless, physiologic feedback control strategy for RBP was developed to mitigate these limitations. The proposed algorithm used intrinsic pump speed to obtain differential pump speed (ΔRPM). The proposed gain-scheduled proportional-integral controller, switching of setpoints between a higher pump speed differential setpoint (ΔRPM Hr ) and a lower pump speed differential setpoint (ΔRPM Lr ), generated pulsatility and physiologic perfusion, while avoiding suction. The switching between ΔRPM Hr and ΔRPM Lr setpoints occurred when the measured ΔRPM reached the pump differential reference setpoint. In-silico tests were implemented to assess the proposed algorithm during rest, exercise, a rapid 3-fold pulmonary vascular resistance increase, rapid change from exercise to rest, and compared with maintaining a constant pump speed setpoint. The proposed control algorithm augmented aortic pressure pulsatility to over 35 mmHg during rest and around 30 mmHg during exercise. Significantly, ventricular suction was avoided, and adequate cardiac output was maintained under all simulated conditions. The performance of the sensorless algorithm using estimation was similar to the performance of sensor-based method. This study demonstrated that augmentation of vascular pulsatility was feasible while avoiding ventricular suction and providing physiological pump outflows. Augmentation of vascular pulsatility can minimize adverse events that have been associated with diminished pulsatility. Mock circulation and animal studies would be conducted to validate these results.

A mathematical model that integrates cardiac electrophysiology, mechanics, and fluid dynamics: Application to the human left heart

We propose a mathematical and numerical model for the simulation of the heart function that couples cardiac electrophysiology, active and passive mechanics and hemodynamics, and includes reduced models for cardiac valves and the circulatory system. Our model accounts for the major feedback effects among the different processes that characterize the heart function, including electro-mechanical and mechano-electrical feedback as well as force-strain and force-velocity relationships. Moreover, it provides a three-dimensional representation of both the cardiac muscle and the hemodynamics, coupled in a fluid-structure interaction (FSI) model. By leveraging the multiphysics nature of the problem, we discretize it in time with a segregated electrophysiology-force generation-FSI approach, allowing for efficiency and flexibility in the numerical solution. We employ a monolithic approach for the numerical discretization of the FSI problem. We use finite elements for the spatial discretization of partial differential equations. We carry out a numerical simulation on a realistic human left heart model, obtaining results that are qualitatively and quantitatively in agreement with physiological ranges and medical images.

Support Pressure Acting on the Epicardial Surface of a Rat Left Ventricle—A Computational Study

The present computational study investigates the effects of an epicardial support pressure mimicking a heart support system without direct blood contact. We chose restrictive cardiomyopathy as a model for a diseased heart. By changing one parameter representing the amount of fibrosis, this model allows us to investigate the impairment in a diseased left ventricle, both during diastole and systole. The aim of the study is to determine the temporal course and value of the support pressure that leads to a normalization of the cardiac parameters in diseased hearts. These are quantified via the end-diastolic pressure, end-diastolic volume, end-systolic volume, and ejection fraction. First, the amount of fibrosis is increased to model diseased hearts at different stages. Second, we determine the difference in the left ventricular pressure between a healthy and diseased heart during a cardiac cycle and apply for the epicardial support as the respective pressure difference. Third, an epicardial support pressure is applied in form of a piecewise constant step function. The support is provided only during diastole, only during systole, or during both phases. Finally, the support pressure is adjusted to reach the corresponding parameters in a healthy rat. Parameter normalization is not possible to achieve with solely diastolic or solely systolic support; for the modeled case with 50% fibrosis, the ejection fraction can be increased by 5% with purely diastolic support and 14% with purely systolic support. However, the ejection fraction reaches the value of the modeled healthy left ventricle (65.6%) using a combination of diastolic and systolic support. The end-diastolic pressure of 13.5 mmHg cannot be decreased with purely systolic support. However, the end-diastolic pressure reaches the value of the modeled healthy left ventricle (7.5 mmHg) with diastolic support as well as with the combination of the diastolic and systolic support. The resulting negative diastolic support pressure is −4.5 mmHg, and the positive systolic support pressure is 90 mmHg. We, thereby, conclude that ventricular support during both diastole and systole is beneficial for normalizing the left ventricular ejection fraction and the end-diastolic pressure, and thus it is a potentially interesting therapy for cardiac insufficiency.

Patient-Specific Computational Fluid Dynamics Reveal Localized Flow Patterns Predictive of Post-Left Ventricular Assist Device Aortic Incompetence

BACKGROUND

Progressive aortic valve disease has remained a persistent cause of concern in patients with left ventricular assist devices. Aortic incompetence (AI) is a known predictor of both mortality and readmissions in this patient population and remains a challenging clinical problem.

METHODS

Ten left ventricular assist device patients with de novo aortic regurgitation and 19 control left ventricular assist device patients were identified. Three-dimensional models of patients' aortas were created from their computed tomography scans, following which large-scale patient-specific computational fluid dynamics simulations were performed with physiologically accurate boundary conditions using the SimVascular flow solver.

RESULTS

The spatial distributions of time-averaged wall shear stress and oscillatory shear index show no significant differences in the aortic root in patients with and without AI (mean difference, 0.67 dyne/cm2 [95% CI, -0.51 to 1.85]; P=0.23). Oscillatory shear index was also not significantly different between both groups of patients (mean difference, 0.03 [95% CI, -0.07 to 0.019]; P=0.22). The localized wall shear stress on the leaflet tips was significantly higher in the AI group than the non-AI group (1.62 versus 1.35 dyne/cm2; mean difference [95% CI, 0.15-0.39]; P<0.001), whereas oscillatory shear index was not significantly different between both groups (95% CI, -0.009 to 0.001; P=0.17).

CONCLUSIONS

Computational fluid dynamics serves a unique role in studying the hemodynamic features in left ventricular assist device patients where 4-dimensional magnetic resonance imaging remains unfeasible. Contrary to the widely accepted notions of highly disturbed flow, in this study, we demonstrate that the aortic root is a region of relatively stagnant flow. We further identified localized hemodynamic features in the aortic root that challenge our understanding of how AI develops in this patient population.

A robust computational framework for estimating 3D Bi-Atrial chamber wall thickness

Atrial fibrillation (AF) is the most prevalent form of cardiac arrhythmia. The atrial wall thickness (AWT) can potentially improve our understanding of the mechanism underlying atrial structure that drives AF and provides important clinical information. However, most existing studies for estimating AWT rely on ruler-based measurements performed on only a few selected locations in 2D or 3D using digital calipers. Only a few studies have developed automatic approaches to estimate the AWT in the left atrium, and there are currently no methods to robustly estimate the AWT of both atrial chambers. Therefore, we have developed a computational pipeline to automatically calculate the 3D AWT across bi-atrial chambers and extensively validated our pipeline on both ex vivo and in vivo human atria data. The atrial geometry was first obtained by segmenting the atrial wall from the MRIs using a novel machine learning approach. The epicardial and endocardial surfaces were then separated using a multi-planar convex hull approach to define boundary conditions, from which, a Laplace equation was solved numerically to automatically separate bi-atrial chambers. To robustly estimate the AWT in each atrial chamber, coupled partial differential equations by coupling the Laplace solution with two surface trajectory functions were formulated and solved. Our pipeline enabled the reconstruction and visualization of the 3D AWT for bi-atrial chambers with a relative error of 8% and outperformed existing algorithms by >7%. Our approach can potentially lead to improved clinical diagnosis, patient stratification, and clinical guidance during ablation treatment for patients with AF.

Impact of myocardial infarction on intraventricular vortex and flow energetics assessed using computational simulations

Flow energetics have been proposed as early indicators of progressive left ventricular (LV) functional impairment in patients with myocardial infarction (MI), but its correlation with individual MI parameters has not been fully explored. Using electro-fluid-structure interaction LV models, this study investigated the correlation between four MI parameters: infarct size, infarct multiplicity, regional enhancement of contractility at the viable myocardium area (RECVM), and LV mechanical dyssynchrony (LVMD) with intraventricular vortex and flow energetics. In LV with small infarcts, our results showed that infarct appearance amplified the energy dissipation index (DI), where substantial viscous energy loss was observed in areas with high flow velocity and near the infarct-vortex interface. The LV with small multiple infarcts and RECVM showed remarkable DI increment during systole and diastole. In correlation analysis, the systolic kinetic energy fluctuation index (E') was positively related to ejection fraction (EF) (R²  = 0.982) but negatively correlated with diastolic E' (R²  = 0.970). Diastolic E' was inversely correlated with vortex kinetic energy (R²  = 0.960) and vortex depth (R²  = 0.876). We showed an excessive systolic DI could differentiate infarcted LV with normal EF from healthy LV. Strong flow acceleration, LVMD, and vortex-infarct interactions were predominant factors that induced excessive DI in infarcted LVs. Instead of causing undesired flow turbulence, high systolic E' suggested the existence of energetic flow acceleration, while high diastolic E' implied an inefficient diastolic filling. Thus, systolic E' is not a suitable early indicator for progressive LV dysfunction in MI patients, while diastolic E' may be a useful index to indicate diastolic impairment in these patients.